Self citation for sure is allowed, but referring to h-index value, in most of cases, is considered without self citation. In h-index value (if you notice to SCOPUS) there is an item to exclude self citation.
In many cases, self citation is needed to help your research become more clear. Also it clears that your research is based on published data and is a continuous target-centred research. I some cases, it also help your paper publishes easier. For instance, if you have published some really interesting and novel data, then based on the papers published you have continued you research, editors are more willing to accept the paper since they feel more readers will be attracted. BUT this does not mean self citation can always help your papers get published, in fact in some rare cases it may help.
I also do not recommend you too much/unnecessary self citation since it does not a have good impact on others judgement about your scientific abilities.
I think you have said well for self citation.
But unnecessary citing own work does not give good impact on the editor.
I wondered to see when reviewers ask "why have not you cited your .... publication?" Sometimes to increase publishers/journal visibility, they suggest the authors to cite own works which is relevant.
Self citation is allowed as you can surely use your own past research work.
This is a great question. Approximately dear Hadi Hezaveh offered perfect answer with details. Thank you.
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